Dr. G wrote:Heiwa:
It is interesting, and very telling, that you dismiss the demolition of the ABC Balzac building as not a ligitimate candidate for your "axiom" because it is (according to you) an example of a collapse with M(upper)/M(lower) ~ 0.5. Your axiom applies (according to you) only to collapses with M(upper)/M(lower) = 0.1.
What about a case with M(upper)/M(lower) = 0.15 ?
Is that outside your axiomatic range?
I have started a thread about it at JREF:
The Heiwa ChallengeIt is assumed at JREF 9/11 Conspiracy Theories Forum that a structure will be crushed, if you drop a piece (1/10th) of the same structure on it and that it is quite normal - no conspiracy. So here is the challenge: Prove it!
Conditions:
1. The structure is supposed to have a certain cross area A and height h and is fixed on the ground. The structure is an assembly of various elements of any type. It can be any size!
2. The structure should be more or less identical from h = 0 to h = h, e.g. uniform density, layout of internal elements, etc. Horizontal elements in structure should be identical. Vertical, load carrying elements should be similar and be uniformly stressed due to gravity, i.e. bottom vertical elements may be reinforced or made a little stronger, if required. Connections between elements should be similar throughout.
3. It is recognized that the structure may be a little higher stressed at h=0 than h=h due to uniform density, elements, etc.
4. Before drop test the structure shall be stable, i.e. carry itself and withstand a small lateral impact at top without falling apart. Connections between elements cannot rely solely on friction.
5. Before test 1/10th of the structure is disconnected at the top at h = 0.9 h without damaging the structure.
6. The lower structure, 0.9 h high is then called part A. The top part, 0.1 h high, is called part C.
7. Mass of part C should be <1/9th of mass of part A.
8. Now drop part C on part A and crush part A (if you can! That's the test).
9. In order to easily repeat the test/challenge drop height should be <1.1 h, i.e. C can only be dropped from 2h above ground on A that is 0.9 h high.
10. Structure is only considered crushed, when >70% of the elements in part A are disconnected from each other after test, i.e. drop by part C on A.
Have a try! I look forward to your structures!
Heiwa
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Dr. G. Re your question M(upper)/M(lower) or C/A one reason for this challenge is to show that the assumption in your BL
GB paper, i.e. that M(upper) or C remains intact during crush down or rubble production of A is not possible. When C produces rubble of A - part B - it also produces rubble ot itself at same rate ... and after a while C is gone! Another reason is to show that rubble of a structure cannot crush the same structure.
I can evidently prove this for various structures but as the number of structures are unlimited I have to make it into an axiom.
C/A = 0.1 is just an arbitrary figure to get the challenge started. C/A = 0.5 can evidently produce a bounce (elastic deformation) - depending on structure and drop height. At a certain drop height (energy input) local failures will also be produced apart from elastic deformation of C and A.
At a bigger drop height you can be sure that C (when C/A = 0.1) is destroyed prior to A.
At an even higher drop height (energy input > total strain energy of C+A)) I wonder what will happen? C is definitely destroyed but will A be completely destroyed? Or is the contact energy wasted somewhere else?
In your BLGB paper it is indicated that C (14 stories) initially applies energy enough to crush say 8 stories of A (total 97 stories) and that after that crush down continues for some strange reasons.
According my experience - applying energy that can crush 8 stories - would result in C being reduced to 10 stories and A to 93 stories and then collision would be arrested. If not, more energy is available because C is still moving, C will continue to be shortened, &c, &c. When all stories of C are rubble, the destruction must be arrested. C doesn't exist any more.
Please, explain where I am wrong!